Problem:
A box contains 2 red, 3 green, and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

Solution:
To find the probability that none of the balls drawn is blue, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:
To find the total number of outcomes, we need to consider all the possible combinations of drawing two balls from the box.

The total number of balls in the box is 2 red + 3 green + 2 blue = 7 balls.

The total number of ways to choose 2 balls out of 7 is given by the combination formula: C(7, 2) = 7! / (2! * (7-2)!) = 21.

Therefore, the total number of possible outcomes is 21.

Favorable outcomes:
To find the number of favorable outcomes, we need to consider the combinations of drawing 2 balls where none of them are blue.

Since there are 2 blue balls, the number of ways to choose 2 balls without selecting any blue ball is given by the combination of choosing 2 balls from the remaining 5 balls (2 red + 3 green).

The number of ways to choose 2 balls out of 5 is given by the combination formula: C(5, 2) = 5! / (2! * (5-2)!) = 10.

Therefore, the number of favorable outcomes is 10.

Probability:
The probability is given by the ratio of the number of favorable outcomes to the total number of outcomes.

Probability = Number of favorable outcomes / Total number of outcomes

Probability = 10 / 21

Therefore, the probability that none of the balls drawn is blue is 10/21.

Answer:
The correct answer is (a) 10/21.